The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
NCERT Class 10 Chapter 12 AREAS RELATED TO CIRCLES
Page No. 225
Exercise 12.1
Question No. 3
Radius of (GOLD region) first circle (r₁) = 21/2 = 10.5 cm
Radius of second circle (r₂) = 10.5 + 10.5 = 21 cm
Radius of third circle (r₃) = 21 + 10.5 = 31.5 cm
Radius of fourth circle (r₄) = 31.5 + 10.5 = 42 cm
Radius of fifth circle (r₅) = 42 + 10.5 52.5 cm
Area of (GOLD region) first circle = πr₁² = π(10.5)² = π(110.25) = 346.50 cm²
Area of RED region = Area of second circle – Area of first circle
= πr₂² – πr₁²
= π(21)² – π(10.5)²
= 4417π – 110.257π
= 330.75π
= 1039.5 cm²
Area of BLUE region = Area of third circle – Area of second circle
= πr₃² – πr₂²
= π(31.5)² – π(21)²
= 992.257π – 441π
= 551.25π
= 1732.5 cm²
Area of BlACK region = Area of fourth circle- Area of third circle
= πr₄² – πr₃²
= π(42)² – π(31.5)²
= 17647π – 992.257π
= 771.75π
= 2425.5 cm²
Area of WHITE region = Area of fifth circle – Area of fourth circle
= πr₅² – πr₄²
= π(52.5)² – π(42)²
= 2756.25π – 1764π
= 992.25π
= 3118.5 cm²
Video explanation 👇😎